# Absolute Value Inequalities – Practice ProblemsHaving fun while studying, practice your skills by solving these exercises!

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Absolute value inequalities can include variable expressions inside the absolute value bars. How do you solve for a variable that’s between the bars?

Similar to absolute value equations with a variable expression inside the absolute value bars, you must set up a positive and negative situation, but look out because inequalities behave differently depending if they are less than or greater than situations (also less than and equal to or greater than and equal to).

For less than situations, an AND situation is created. To reflect |x| < v, set up a positive and negative inequality: –v < x AND x < v. Solve for both, and graph the two solutions on a number line; the solution to the absolute value inequality is the intersection of the two solutions. You will notice the graph has a distinctive appearance, as only one section of the graph is shaded.

For greater than situations, an OR situation is created. To reflect |x| > v, set up a positive and negative inequality: x < -v OR x > v. Solve for both, and graph the two solutions on a number line; the solution to the absolute value inequality is the union of the two solutions. Just like before, the graph has a distinctive appearance, but this time it’s shaded in two separate sections.

When inequalities contain AND and OR solutions they are also called compound inequalities. Often, students find this topic challenging, but if you watch out for the pattern of AND and OR situations, you’ll be okay but just in case, watch this video to discover the cure for absolute value inequality headaches.

Represent and solve equations with absolute value.

CCSS.MATH.CONTENT.HSA.REI.D.11

Exercises in this Practice Problem
 Evaluate the absolute value inequality. Identify the critical body temperature range. Assign the absolute value inequality its corresponding number line. Determine the dangerous and critical temperatures. Analyze the absolute value inequalities. Solve the following absolute value inequalities.